$Z_n$ symmetry in the vortex muon decay

TL;DR

This paper explores the polarization structure of vortex muons with $Z_n$ symmetry, revealing that their decay electron distribution preserves this symmetry, offering insights into exotic fermion states.

Contribution

It introduces a novel vortex muon state with $Z_n$ symmetry and analyzes how this symmetry influences decay electron distributions.

Findings

Electron azimuthal distribution exhibits $Z_n$ symmetry.

Vortex muons can be prepared in exotic polarized states.

Decay patterns reflect initial polarization symmetry.

Abstract

Polarization of a vortex state fermion has rich structure due to the nontrivial momentum distribution of wave function. This larger freedom provides an unique opportunity to prepare fermions in exotic polarized states, which do not exist for plane-wave state fermions. Based on the so called spin-orbit state which was studied both theoretically and experimentally, we put forward a peculiar vortex muon whose polarization exhibits $Z_n$ symmetry and study its decay. We investigate the azimuthal distribution of the emitted electrons and find that it exhibits the same symmetry ($Z_n$) as the initial state.